Question

Find a basis for the nullspace of the matrix. If there is no basis, enter 'none' in any single cell.

a = 5 3 1
0 1 0

Answer 1

To find the basis for the nullspace of a matrix, set up the equation Ax = 0 and solve for x. For the given matrix, the nullspace is spanned by the vector (-3, 0, 1), giving us a basis for the nullspace.

Step-by-step explanation:

To find the basis for the nullspace of a matrix, we need to find all the solutions to the equation Ax = 0, where A is the matrix and x is a column vector.

In this case, the matrix A is given as:

531010

We can set up the equation Ax = 0 as:

531010x1x2x3 = 00

Solving this equation, we find that the nullspace of the matrix is spanned by the vector x = (-3x3, 0, x3), where x3 is any real number. Therefore, a basis for the nullspace is {(-3, 0, 1)}.